Phase transition to blob-hole coherent structure in the Hasegawa–Mima model for plasmas

2021 ◽  
Vol 87 (6) ◽  
Author(s):  
Chjan C. Lim
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Critical Temperature ◽  
Partition Function ◽  
Open System ◽  
Ground State ◽  
Spherical Model ◽  
Toroidal Plasmas ◽  
Fixed Energy ◽  
System A

An equilibrium statistical mechanics theory for the Hasegawa–Mima equations of toroidal plasmas, with canonical constraint on energy and microcanonical constraint on potential enstrophy, is solved exactly as a spherical model. The use of a canonical energy constraint instead of a fixed-energy microcanonical approach is justified by the preference for viewing real plasmas as an open system. A significant consequence of the results obtained from the partition function, free energy and critical temperature, is the condensation into a ground state exhibiting a blob-hole-like structure observed in real plasmas.

Possible Bose-Einstein Condensation of Polygonal Clusters in 2D-Materials

2019 ◽  
Vol 297 ◽  
pp. 204-208
Author(s):  
Abid Boudiar
Keyword(s):  
Free Energy ◽  
Critical Temperature ◽  
Ground State ◽  
Low Temperatures ◽  
2D Materials ◽  
Equilibrium Structure ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Exchange Approximation ◽  
Bose Einstein

This study investigates the possibility of Bose-Einstein condensation (BEC) in 2D-nanoclusters. A ground state equilibrium structure involves the single phonon exchange approximation. At critical temperature, the specific heat, entropy, and free energy of the system can be determined. The results support the existence of BEC in nanoclusters, and they lead to predictions of the behaviour of 2Dmaterials at low temperatures.

SIGNATURES OF AN EMERGENT GRAVITY FROM BLACK HOLE ENTROPY

2009 ◽  
Vol 18 (14) ◽  
pp. 2323-2327
Author(s):  
CENALO VAZ
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Mass Spectrum ◽  
Partition Function ◽  
Ground State ◽  
Degrees Of Freedom ◽  
Thermodynamic Description ◽  
Black Hole Entropy ◽  
Fundamental Particle ◽  
Horizon Radius

The existence of a thermodynamic description of horizons indicates that space–time has a microstructure. While the "fundamental" degrees of freedom remain elusive, quantizing Einstein's gravity provides some clues about their properties. A quantum AdS black hole possesses an equispaced mass spectrum, independent of Newton's constant, G, when its horizon radius is large compared to the AdS length. Moreover, the black hole's thermodynamics in this limit is inextricably connected with its thermodynamics in the opposite (Schwarzschild) limit by a duality of the Bose partition function. G, absent in the mass spectrum, re-emerges in the thermodynamic description through the Schwarzschild limit, which should be viewed as a natural "ground state." It seems that the Hawking–Page phase transition separates fundamental, "particle-like" degrees of freedom from effective, "geometric" ones.

scholarly journals Exact Solution of a One-dimensional Spin System

1970 ◽  
Vol 23 (5) ◽  
pp. 927 ◽  
Author(s):  
RW Gibberd
Keyword(s):  
Phase Transition ◽  
Exact Solution ◽  
Free Energy ◽  
Partition Function ◽  
Thermodynamic Limit ◽  
Spin System ◽  
Spin Systems ◽  
One Dimensional ◽  
Gibb’S Free Energy ◽  
Theory Of Superconductivity

The partition function and the Gibb's free energy are calculated exactly in the thermodynamic limit, using techniques which are well known in the theory of superconductivity. This calculation illustrates explicitly the similarity between the phase transition in superconductivity and the molecular field transitions in spin systems.

scholarly journals The Surrounded Atom Theory of Order-disorder Phase Transition in Binary Alloys

2011 ◽  
Vol 21 (3) ◽  
pp. 265
Author(s):  
Do Chieu Ha ◽  
Nguyen Nhat Khanh
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Critical Temperature ◽  
Binary Alloys ◽  
Disorder Phase Transition ◽  
Atom Model ◽  
Atom Theory

In this paper, the surrounded atom model is developed to study the order-disorder phase transition in binary alloys. We calculate the configurational free energy of the alloys, derive the equation of equilibrium and determine the critical temperature of the phase transition.

scholarly journals STRING CORRECTIONS TO THE HAWKING–PAGE PHASE TRANSITION

1999 ◽  
Vol 14 (05) ◽  
pp. 379-385 ◽  
Author(s):  
KARL LANDSTEINER
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Free Energy ◽  
Critical Temperature ◽  
String Theory ◽  
Hole Radius ◽  
String Corrections ◽  
Type Iib String Theory

We compute the O(α′3) corrections to the AdS5 black hole metric in type IIB string theory. Contrary to previous work in this direction we keep the black hole radius finite. Thus the topology of the boundary is S3×S1. We find the corrections to the free energy and the critical temperature of the phase transition.

scholarly journals Spherical model and quantum phase transitions

2021 ◽  
Vol 2094 (2) ◽  
pp. 022027
Author(s):  
V N Udodov
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Critical Temperature ◽  
Critical Exponents ◽  
Quantum Phase Transitions ◽  
Dimensional Space ◽  
Spherical Model ◽  
Quantum Phase ◽  
Two Dimensional ◽  
Epsilon Expansion

Abstract The spherical Berlin-Katz model is considered in the framework of the epsilon expansion in one-dimensional and two-dimensional space. For the two-dimensional and threedimensional cases in this model, an exact solution was previously obtained in the presence of a field, and for the two-dimensional case the critical temperature is zero, that is, a “quantum” phase transition is observed. On the other hand, the epsilon expansion of critical exponents with an arbitrary number of order parameter components is known. This approach is consistent with the scaling paradigm. Some critical exponents are found for the spherical model in one-and twodimensional space in accordance with the generalized scaling paradigm and the ideas of quantum phase transitions. A new formula is proposed for the critical heat capacity exponent, which depends on the dynamic index z, at a critical temperature equal to zero. An expression is proposed for the order of phase transition with a change in temperature (developing the approach of R. Baxter), which also depends on the z index. An interpolation formula is presented for the effective dimension of space, which is valid for both a positive critical temperature and a critical temperature equal to zero. This formula is general. Transitions with a change in the field in a spherical model at absolute zero are also considered.

scholarly journals Groups, groupoids, and information sources: models of mitochondrial deterioration and aging

2014 ◽  
Author(s):  
Rodrick Wallace
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Ground State ◽  
Information Sources ◽  
Error Minimization ◽  
Biological Processes ◽  
Coding Scheme ◽  
Energy Delivery ◽  
Living State

Using mitochondrial free energy delivery rate as a temperature analog, we examine the 'spontaneous symmetry breaking' of the group associated with the error minimization coding scheme related to protein folding, and characterize the phase transition that drives the collapse of normal folding to pathological amyloid production. Similarly, groupoids prove central to the study of analogous, often highly punctuated, 'ground state' failures in far more complex biological processes, adopting Maturana's perspective on the central role of cognition throughout the living state.

scholarly journals Groups, groupoids, and information sources: models of mitochondrial deterioration and aging

2014 ◽  
Author(s):  
Rodrick Wallace
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Ground State ◽  
Information Sources ◽  
Error Minimization ◽  
Biological Processes ◽  
Coding Scheme ◽  
Energy Delivery ◽  
Living State

Using mitochondrial free energy delivery rate as a temperature analog, we examine the 'spontaneous symmetry breaking' of the group associated with the error minimization coding scheme related to protein folding, and characterize the phase transition that drives the collapse of normal folding to pathological amyloid production. Similarly, groupoids prove central to the study of analogous, often highly punctuated, 'ground state' failures in far more complex biological processes, adopting Maturana's perspective on the central role of cognition throughout the living state.

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

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